$D$-dimensional Bardeen-AdS black holes in Einstein-Gauss-Bonnet theory

TL;DR

This paper introduces a new class of $D$-dimensional Bardeen-like AdS black holes in Einstein-Gauss-Bonnet gravity, analyzing their thermodynamics, extremal conditions, and phase transitions, revealing stable remnants after evaporation.

Contribution

The study presents exact solutions for $D$-dimensional Bardeen-EGB-AdS black holes, including their thermodynamic properties and critical behavior, which was not previously known.

Findings

Existence of a critical charge $e_E$ for extremal black holes.

Divergence of heat capacity at a critical horizon radius.

Black hole evaporation results in thermodynamically stable remnants.

Abstract

We present a $D$-dimensional Bardeen like Anti-de Sitter (AdS) black hole solution in Einstein-Gauss-Bonnet (EGB) gravity, \textit{viz}., Bardeen-EGB-AdS black holes. The Bardeen-EGB-AdS black hole has an additional parameter due to charge ($e$), apart from mass ($M$) and Gauss-Bonnet parameter ($\alpha$). Interestingly, for each value of $\alpha$, there exist a critical $e = e_E$ which corresponds to an extremal regular black hole with degenerate horizons, while for $e< e_E$, it describes non-extremal black hole with two horizons. Despite the complicated solution, the thermodynamical quantities, like temperature ($T$), specific heat($C$) and entropy ($S$) associated with the black hole are obtained exactly. It turns out that the heat capacity diverges at critical horizon radius $r_+ = r_C$, where the temperature attains maximum value and the Hawking-Page transition is achievable. Thus, we have an exact $D$-dimensional regular black holes, when evaporates lead to a thermodynamical stable remnant.